traj_gen-matlab

Optimal trajectory generation

traj_gen is a continuous trajectory generation package where high order derivatives along the trajectory are minimized while satisfying waypoints (equality) and axis-parallel box constraint (inequality). The objective and constraints are formulated in quadratic programming (QP) to cater the real-time performance.

To parameterize a trajectory, we use two types of curve: 1) piecewise-polynomials [1,2] and 2) a sequence of points [3]. The difference is optimization variables.

a. Piecewise-polynomials (polyTrajGen class) : It defines the primitive of the curve as polynomical spline. The optimization target is either polynomial coefficients [1] or free end-derivatives of spline segments [2] (can be set in constructor). In general, the latter has fewer optimization variables as it reduces the number of variable as much as the number of equality constraints.
b. A sequence of points (optimTrajGen class) : It does not limit the primitive of the curve. The optimization target is a finite set of points. The final curve is defined as a linear interpolant of the set of points. The point density (# of points per time) should be set in the constructor. Instead of unlimited representation capability of a curve, the size of optimization is driectly affected by the point density.

In this package, we use pin to accommodate the two constraints: equality (fix pin) and inequality (loose pin). Pin can be imposed regardless of the order of derivatives. Fix-pin refers a waypoint constraint, and loose-pin denotes a axis-parallel box constraint. The pin is a triplets (time (t), order of derivatives (d), value (x)) where x is a vector in case of fix-pin while two vectors [xl xu] for the loose-pin.

[1] Mellinger, Daniel, and Vijay Kumar. "Minimum snap trajectory generation and control for quadrotors." 2011 IEEE International Conference on Robotics and Automation. IEEE, 2011.

[2] Richter, Charles, Adam Bry, and Nicholas Roy. "Polynomial trajectory planning for aggressive quadrotor flight in dense indoor environments." Robotics Research. Springer, Cham, 2016. 649-666.

[3] Ratliff, Nathan, et al. "CHOMP: Gradient optimization techniques for efficient motion planning." 2009 IEEE International Conference on Robotics and Automation. IEEE, 2009.